I have just begun a course on number theory and proofs, and I need help with the process of solving Diophantine equations. I am not sure how to employ the Euclidean algorithm to solve the following equation or how to go from that to the next step.
2011x + 1492y = 10,000
Could someone please explain the process to me? I need to determine whether this has integer solutions, but more importantly, I need to be able to understand and use this process on other such problems.
Thank you very much for your time.